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Bayes model averaging with selection of regressors

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  • P. J. Brown
  • M. Vannucci
  • T. Fearn

Abstract

When a number of distinct models contend for use in prediction, the choice of a single model can offer rather unstable predictions. In regression, stochastic search variable selection with Bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors. Here we look at Bayes model averaging incorporating variable selection for prediction. This offers similar mean-square errors of prediction but with a vastly reduced predictor space. This can greatly aid the interpretation of the model. It also reduces the cost if measured variables have costs. The development here uses decision theory in the context of the multivariate general linear model. In passing, this reduced predictor space Bayes model averaging is contrasted with single-model approximations. A fast algorithm for updating regressions in the Markov chain Monte Carlo searches for posterior inference is developed, allowing many more variables than observations to be contemplated. We discuss the merits of absolute rather than proportionate shrinkage in regression, especially when there are more variables than observations. The methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution. Copyright 2002 Royal Statistical Society.

Suggested Citation

  • P. J. Brown & M. Vannucci & T. Fearn, 2002. "Bayes model averaging with selection of regressors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 519-536.
  • Handle: RePEc:bla:jorssb:v:64:y:2002:i:3:p:519-536
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    References listed on IDEAS

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    1. Merlise Clyde & Edward I. George, 2000. "Flexible empirical Bayes estimation for wavelets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 681-698.
    2. Rolf Sundberg, 1999. "Multivariate Calibration - Direct and Indirect Regression Methodology," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 161-207.
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    Citations

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    Cited by:

    1. Simila, Timo & Tikka, Jarkko, 2007. "Input selection and shrinkage in multiresponse linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 406-422, September.
    2. Theo S. Eicher & Chris Papageorgiou & Adrian E. Raftery, 2011. "Default priors and predictive performance in Bayesian model averaging, with application to growth determinants," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 30-55, January/F.
    3. D. Fouskakis & I. Ntzoufras & D. Draper, 2009. "Population-based reversible jump Markov chain Monte Carlo methods for Bayesian variable selection and evaluation under cost limit restrictions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 383-403.
    4. Korobilis, Dimitris, 2008. "Forecasting in vector autoregressions with many predictors," MPRA Paper 21122, University Library of Munich, Germany.
    5. Chen, Kun & Jiang, Wenxin & Tanner, Martin A., 2010. "A note on some algorithms for the Gibbs posterior," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1234-1241, August.
    6. ter Braak, Cajo J.F., 2006. "Bayesian sigmoid shrinkage with improper variance priors and an application to wavelet denoising," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1232-1242, November.
    7. Oliver J. Rutz & Michael Trusov & Randolph E. Bucklin, 2011. "Modeling Indirect Effects of Paid Search Advertising: Which Keywords Lead to More Future Visits?," Marketing Science, INFORMS, vol. 30(4), pages 646-665, July.
    8. Nott, David J. & Leng, Chenlei, 2010. "Bayesian projection approaches to variable selection in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3227-3241, December.
    9. Hongxiao Zhu & Marina Vannucci & Dennis D. Cox, 2010. "A Bayesian Hierarchical Model for Classification with Selection of Functional Predictors," Biometrics, The International Biometric Society, vol. 66(2), pages 463-473, June.
    10. Steven N. Durlauf & Andros Kourtellos & Chih Ming Tan, 2005. "How Robust Are the Linkages Between Religiosity and Economic Growth," Discussion Papers Series, Department of Economics, Tufts University 0510, Department of Economics, Tufts University.
    11. Ander Wilson & Brian J. Reich, 2014. "Confounder selection via penalized credible regions," Biometrics, The International Biometric Society, vol. 70(4), pages 852-861, December.
    12. Ouysse, Rachida & Kohn, Robert, 2010. "Bayesian variable selection and model averaging in the arbitrage pricing theory model," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3249-3268, December.

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